# [Ifeffit] Phase corrected Fourier transforms

Kelly, Shelly D. SKelly at anl.gov
Sun Sep 24 09:15:31 CDT 2006

```Hi Juan and John,

Here us my 2cents worth...

Unfortunately the magnitude of the FT is not as simple as a RDF.  I agree with John that the ultimate goal of the analysis is to come up with a RDF.  But I disagree about the worth of adding a bit more processing to the spectra that makes the spectra just a bit more like an RDF but leaves the data so far from it, such that true analysis is still needed.  If the phase shift correction actually allowed the spectra to be inverted, we would all do it!

I started a page the XAFS.org page under tutorials about the information that should be reported with EXAFS spectra.  On that page I added a link to some of my favorite rants, including a section about why the Magnitude of the FT is not a radial distribution function. http://xafs.org/Common_Mistakes I encourage everyone on the list to read and change these pages and add your own pages.  I think that this is a really great way to come up with a community voice.

Here are a few thoughts about why I don't favor adding the phase shit.
(1) Often 2nd and 3rd neighboring peaks don't turn-up as peaks at all in the FT because of the interference between themselves and the strong signal from the first shell.  In this case the "peak" is a shoulder or sometimes even the opposite of a shoulder were the first peak is shaved off on the side.  The phase correction isn't going to fix that.  As John mentioned (2) multiple scattering paths are not supposed to be in a radial distribution function and they often show up as peaks in the Mag of the FT and (3) some signals are not a single peak, but a doublet in the magnitude of the FT.  The phase correction doesn't "fix" multiple scattering paths or the doublets.  I'm not sure that I want the multiple scattering paths fixed, they often have a lot of information in them. (4) A Fourier transform will never be able to tell the difference between neighboring atom types as a radial distribution function.  (5) In addition the phase correction in Athena only corrects for half of the phase shift, the part from the central atom.  The other half of the phase shift comes from the scattering atom type, which can only be corrected in Artemis.

I do not recommend using the phase shit option in Athena because it does not turn the data into a radial distribution function.  The magnitude of the FT is only an envelope function. A lot of information within the spectra is not displayed in the magnitude of the FT.  It is the chi(k), and the real and imaginary parts of the FT which show the complexity of the spectroscopy.  I think that this complexity should be embraced not hidden.

In John's language, I think that the picture is more blurred by adding a phase correction to the spectra mainly because it promises so much but actually adds so little.  It seems to me that adding the phase shit, indicates that there is something inherently "wrong" with the Magnitude of the Fourier transform of the spectra.  I don't endorse that point of view. Truly, a radial distribution function is the goal of most analysis, so I encourage the display of the individual contributions/paths to the total model.  I think that this display of all the paths particularly in the chi(k), real and/or imaginary parts of the FT adds a lot of transparency to the data analysis and interpretation.

Well, Juan you walked right into that one.   Welcome to the mailing list...:)

Shelly

-----Original Message-----
From: ifeffit-bounces at millenia.cars.aps.anl.gov [mailto:ifeffit-bounces at millenia.cars.aps.anl.gov] On Behalf Of John J. Rehr
Sent: Saturday, September 23, 2006 11:01 PM
To: XAFS Analysis using Ifeffit
Cc: John J. Rehr; anatoly.frenkel at yu.eduA
Subject: RE: [Ifeffit] Phase corrected Fourier transforms

Anatoly is correct that the phase correction cannot work for all shells
in inhomogeneous systems. However, it's *always* possible to remove the
central atom phase shift 2 delta_c which often dominates the phase
correction. Second, if one corrects by the 1st nn phase, delta_1, the dominant
near neighbor shell will appear at the correct distance. The correction
is not right for subsequent shells but the error is given by a phase
difference
delta R = <(1/2)(d/dk) [delta_n-delta_1]>
This correction is typically order 0.1 Ang and usually smaller than the
typical shift of about 0.3 - 0.4 Ang in uncorrected FT peaks.

The upshot is that the phase corrected FT can be correct for the first shell
which often dominates the FT and generally better than uncorrected FTs.

Corrective lenses for vision aren't perfect either at all distances,
but it's hard to argue that it's preferable not to use them for that
reason.

J. Rehr

On Sat, 23 Sep 2006, Anatoly Frenkel wrote:

> My 0.533 Rouble: In my experience with some Mn oxides, the Mn-O FT magnitude
> peak's position is 0.5 A lower its corresponding 1NN bond length, while the
> Mn-Mn are 0.3 A lower than their bond lenghts. Thus, it would be misleading
> for this and other similar compounds to apply theoretical phase correction
> of the 1NN to the entire data, as it will shift only one peak correctly.
>
> Anatoly
>
> -----Original Message-----
> From: ifeffit-bounces at millenia.cars.aps.anl.gov
> [mailto:ifeffit-bounces at millenia.cars.aps.anl.gov]On Behalf Of Matthew
> Marcus
> Sent: Saturday, September 23, 2006 4:14 PM
> To: XAFS Analysis using Ifeffit
> Subject: Re: [Ifeffit] Phase corrected Fourier transforms
>
>
> OK, I have to put in my US\$0.02/e0.02.  The phase correction can't mean much
> if the scattering atoms are different, which is usually
> the case.  If the scattering atoms are very heavy, then the phase correction
> has a kink in it which could cause strange shapes if applied
> to light-atom shells.  I've played with this phase correction and amplitude
> correction, while I was at it, and not been very impressed.
> One place where it might be useful is in the aforementioned case of heavy
> and light scatterers.  If you use the correction for one of
> these, then the corresponding shells sharpen and the other ones blur out, so
> you can get a rough idea of who's who.  I suspect
> this works better if you do the amplitude as well.
>
> A related technique is to use model compounds+FEFF to get 'semi-empirical'
> amps and phases which include all the artifacts
> of the experiment.  Suppose, for instance, that you're looking at Cu in a
> matrix of Fe, and you have data for Cu metal but
> not for any known Cu->Fe scattering pair.  You can synthesize a
> 'semi-empirical' Cu->Fe phase and amp like this:
>
> phi(Cu->Fe) = phi_exp(Cu->Cu)+(phi_theor(Cu->Fe)-phi_theor(Cu->Cu))
> amp(Cu->Fe) = amp_exp(Cu->Cu)*amp_theor(Cu->Fe)/amp_theor(Cu->Cu)
>
> If you don't want to do this for modeling, you can use this method for
> comparing two spectra which you think might
> be alike except for the central atom, by "correcting" one spectrum with the
> difference to make it comparable to the other.
>
> Another aspect to this whole thing is that people are very used to
> uncorrected FT's and are aware that you have to add 0.3-0.4A
> to the distances.  If you show only corrected FT's, I wonder if that will be
> satisfying to the audience.
>    mam
>
> ----- Original Message -----
> From: "John J. Rehr" <jjr at leonardo.phys.washington.edu>
> To: "XAFS Analysis using Ifeffit" <ifeffit at millenia.cars.aps.anl.gov>
> Cc: "John J. Rehr" <jjr at phys.washington.edu>
> Sent: Saturday, September 23, 2006 7:18 AM
> Subject: Re: [Ifeffit] Phase corrected Fourier transforms
>
>
>
> Dear Juan Antonio,
>
>  I personally feel that adding phase correction to the XAFS FT is
> highly desirable, and I encouraged its implementation in Athena.
> The reasons are the following:
>
> 1) Peaks in  non-phase corrected FT are substantially in error.
> 2) The non-linearity of the phase shifts in high-Z materials leads
> to multiple-peaks, thus blurring the FT.
> 3) Theoretical phase shifts are good enough that adding phase correction
> tends to correct the peak positions and the problems due to non-linearities.
> 4) Adding phase correction does no-harm to the fits. That is, one gets
> the same results whether or not phase correction is included.
> 5) Adding phase correction gives a FT which can be more easily
> interpreted "by eye", that is the peaks have a more physical interpretation.
> On the contrary, non-phase corrected FTs can be mis-interpreted.
>
> Overall, my view is that the phase correction is like a prescription
> lens which gives a sharper image. While the image may not be perfect,
> at least it's generally much superior to the non-phase corrected FT.
>
>  J. Rehr
>
> On Fri, 22 Sep 2006, Juan Antonio [iso-8859-1] Maciá Agulló wrote:
>
>>
>>
>> Hi all,
>>
>> I have read Phase corrected Fourier transforms in Athena manual and now
>> I have a big doubt, ¿phase correction or not in a publication?
>>
>> I have read also that this correction is different (more complete) in
>> Artemis and I am not sure if I should correct also in Artemis and which
>> path should I use and why.
>>
>> I saw many papers dealing with EXAFS fits and they showed a "calculated"
>> bond distance, I think it is: d = Reff + deltaR, right?
>>
>> I also ask for a paper where I can find that deltaE is ok (even for
>> high-Z backscatterers) if deltaE < 10eV.
>>
>> I have high correlations between ss and SO2, and deltaR and deltaE. I
>> tried different fits but I can not eliminate them, then...is the fit
>> wrong?
>>
>> Sorry for these easy questions but I am a novice in XAFS.
>>
>> Thank you very much.
>>
>> Best regards,
>> JA
>>
>
>
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